Examples of Chaotic Dynamics

Chaos on the Real Number Line

Functions dealing with the real number line are probably what you are most familiar with. These functions take R¹ R¹, meaning that the real number line (R¹) is being mapped to the real number line. (See Function Basics - Algebra) A good example of one of these functions is the quadratic family.

• The Quadratic Family - A group of typical R¹ R¹ functions, analyzed for bifurcations.
• The Cantor Set - A group of points on the real number line that have interesting properties.

Chaos in the Plane

• The Sierpenski Triangle and its Area - very much like the Cantor set

Chaos on the Complex Plane

• The Mandelbrot Set - A group of complex numbers that do not diverge under certain conditions.
• The Julia Sets - Sets of complex numbers that do not escape to infinity under iteration.